Triple weave is also called 3 rod wale. The same principle applies for 4, 5, or 6 (weavers) rod waling. I learned from Flo Hoppe's book Wicker Basketry. These are right hand instructions cause, you guessed it, I'm right-handed. It is used for strength and locking the spokes into place.

Tie a colored twist tie on three consecutive spokes (or rods as the English walers called it)
going to the right. they are now number 1 2 and 3. Mark the 3 left spokes next to these going to the left with a different color tie. Call these x y z, so now you have 6 spokes all designated x y z 1 2 3.

To start you put a weaver behind spoke 1 on its right side so it lays between spoke 1 and 2, another weaver is placed beside spoke 2, resting between 2 and 3. The third weaver is placed beside spoke 3 resting between 3 and 4.

Weaving will be to the right around the basket, but you are starting with weaver number 1 which is to the far left of spokes 1 2 and 3. Take the first weaver number 1 and go in front of (or over) spokes number 2 and 3, go behind the next spoke and bring the weaver out to the front. It is now filling what was an empty space between spokes 4 and 5.

(weavers now in order 2 3 1)

Again we take the weaver that is the furthest to the left of the weavers, and now that is weaver number 2, it goes over spokes 3 and 4 into the basket and back out to the front
on the right side of spoke 5 so it is laying between spokes 5 and 6

(weavers now in order 3 1 2)

To complete the first sequence, we again take the weaver furthest to the left which is now weaver 3. It goes over spokes 4 and 5 into the basket and back out to the front on the right side of spoke 6 and is laying between spokes 6 and 7.

(your weavers are now back into position as 1 2 3)

Continue again around repeating more sequences till you get to where you have a weaver sitting in the space just to the right of spoke 1 (Z spoke 1 )

Now you do what is called a "step up." It is to adjust the rod you can't see any difference in the weaving as you can sometimes can find the start of each row of twining.

Anyhow, now the rules change just for this one spot only!!!!

You now have three weavers to the left of spoke 1 sitting in spaces beside spokes x y z
We will count them for this step only weavers 3 2 1. We will take weaver 1 which is on the Right side of the weavers and take it in front of spokes 1 and 2 into the basket and back out to sit in spaces 3 and 4

Take the next weaver to the right which is 2 and weave over Z and 1 into the basket and out to lie in spaces beside spoke 2 and 3

Now we take the last weaver 1 and go over spoke W and Z back into the basket and out to lay in spaces besides spoke 1 and 2

Now our weavers are back in the order we had for the start of the first row so I now start my second row using the weaver that is furthest to the left number 1.

If you are only doing 1 row of three rod or when you are finishing your last row you would just lay in the weaver when you go into the basket and not bring them back out to the front
Cut them off about 1 to 2 inches long and trim later.